Inserted: 17 mar 2009
Last Updated: 31 mar 2009
In the class of Carnot groups we study fine properties of sets of finite perimeter. Improving a recent result by Ambrosio-Kleiner-Le Donne, we show that the perimeter measure is local, i.e. that given any pair of sets of finite perimeter their perimeter measures coincide on the intersection of their essential boundaries. As a consequence we prove a general chain rule for $BV$ functions in this setting.
Keywords: Carnot groups, Sets of finite perimeter, BV functions